Torsion of functionally graded hollow tubes of polygonal shape

In this paper, a simple formulation is presented for torsional analysis of functionally graded hollow tubes of polygonal shape. Normalized shear stress and normalized angle of twist are obtained by this formulation. Governing equations and boundary conditions in term of Prandtl’s stress function are used to derive the formulas. Formulas are so explicit and simple that calculations can be carried out by a pocket calculator. Thicknesses of all segments of the cross section are the same and the shear modulus of rigidity changes continuously across the thickness according to a power law distribution between metal and ceramic phases. Several examples are presented to show the accuracy and efficiency of the formulation. Results are verified by accurate finite element solution. Effects of changing thickness and power law exponent - volume fraction of the constituent materials - are also investigated. Derived formulas can be useful for analysis of thin to moderately thick-walled FGM hollow tubes of polygonal shape.